ZA will be near death at this point. Use #2 to maintain the speed debuff. Most of the time Honky-Tonky will choose to use its Lock-On, so you can use #3 before ZA dies and have things nicely set up for ZK.

Assuming you managed to get both debuffs rolling, immediately use HP. If not, use BC first and then HP.

Depending on step #4, you may not get Honk-Tonk defeated before ZK dies. But don't worry, just use whatever ability works best to finish off Hony-Tonk.

By this point, ZK will definitely be dead, leaving your Darkmoon Tonk. Use Shock and Awe for its medium damage and the chance at stun. At this point, I spam Lock-On despite the two rounds it takes due to its heavy damage.

DMT may die, but it will resurrect one time due to its racial. Getting through one more attack should finish the battle.

(This is RNG dependent, and what I personally use because I don't have the pets that better suit the fight!)

Blizzard broke god-combo, alas. Original strat is in spoiler.

I now use Zandalari Anklerender, Phoenix Hatchling, and Pandaren Water Spirit, and just try to follow Alayea's strategy.

I used Pandaren Water Spirit, Chrominius, and Arcane Eye. Set up the first two pets as Alayea describes. Arcane Eye should be set up for Focused Beams, Eyeblast, and Mana Surge. Follow Alayea's steps and it should (barring bad RNG) see you defeat Judgement and Honky Tonk.

Now, for Fezwick: Cast one last Geyser using PWS before it dies to Fezwick. Arcane Eye will come forward. Immediately use Eyeblast! Fezwick is very fast, and your battle pet will only survive if you slow the monkey down. Follow up with either one of the other two abilities Arcane Eye has available. With luck, you'll defeat Jeremy Feasel's last battle pet.

Today ended up having better success and a much easier time with a Celestial Dragon (against Judgement), Fel Flame (against Honky-Tonk) and Gilnean Raven (against the blasted Fezwick). The raven probably wasn't even the best choice against him, I just really wanted the revenge of using Nevermore on him.

I used Zandalari Anklerender, Zandalara Footslasher (since my Kneebiter is way too low, with Hunting Pary, Leap and Bloodfang) and the Darkmoon Tonk. The Footslasher managed to live long enough to use Bloodfang, and the tonk's Shock-and-Awe took out he last pet.